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arXiv · 2509.04709

Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate

Aijun Yang·Mary Lesperance·Farouk S. Nathoo
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Abstract

This paper considers estimation for linear regression analysis with covariate measurement error arising from Poisson surrogates. We consider cases where covariates follow a conditional Poisson distribution, capturing non-Gaussian and heteroscedastic error structures. To address this, we extend the simulation extrapolation (SIMEX) algorithm to the conditional Poisson setting (POI-SIMEX), enabling robust adjustment in the absence of internal validation data. Theoretical analysis establishes strong consistency of the POI-SIMEX estimator under a linear regression framework.

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Aijun Yang, Mary Lesperance, Farouk S. Nathoo. 2025-09-04. Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate. https://arxiv.org/abs/2509.04709

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